AI News, Artificial Neural Networks/Neural Network Basics

Artificial Neural Networks/Neural Network Basics

Artificial Neural Networks, also known as “Artificial neural nets”, “neural nets”, or ANN for short, are a computational tool modeled on the interconnection of the neuron in the nervous systems of the human brain and that of other organisms.

Artificial neural networks are very different from biological networks, although many of the concepts and characteristics of biological systems are faithfully reproduced in the artificial systems. Artificial

neural nets are a type of non-linear processing system that is ideally suited for a wide range of tasks, especially tasks where there is no existing algorithm for task completion.

With proper training, ANN are capable of generalization, the ability to recognize similarities among different input patterns, especially patterns that have been corrupted by noise.

The term “Neural Net” refers to both the biological and artificial variants, although typically the term is used to refer to artificial systems only.

Each neuron is a multiple-input, multiple-output (MIMO) system that receives signals from the inputs, produces a resultant signal, and transmits that signal to all outputs.

However, to reproduce the effect of the synapse, the connections between PE are assigned multiplicative weights, which can be calibrated or “trained” to produce the proper system output.

Where ζ is the weighted sum of the inputs (the inner product of the input vector and the tap-weight vector), and σ(ζ) is a function of the weighted sum.

If we recognize that the weight and input elements form vectors w and x, the ζ weighted sum becomes a simple dot product:

The dotted line in the center of the neuron represents the division between the calculation of the input sum using the weight vector, and the calculation of the output value using the activation function.

Neural networks tend to have one input per degree of freedom in the input space, and one output per degree of freedom in the output space.

Expert systems, by contrast, are used in situations where there is insufficient data and theoretical background to create any kind of a reliable problem model.

Expert systems emulate the deduction processes of a human expert, by collecting information and traversing the solution space in a directed manner.

Though such assumptions are not required, it has been found that the addition of such a priori information as the statistical distribution of the input space can help to speed training.

During training, the neural network performs the necessary analytical work, which would require non-trivial effort on the part of the analyst if other methods were to be used.

learning paradigm is supervised, unsupervised or a hybrid of the two, and reflects the method in which training data is presented to the neural network.

A learning rule is a model for the types of methods to be used to train the system, and also a goal for what types of results are to be produced.

During training, care must be taken not to provide too many input examples and different numbers of training examples could produce very different results in the quality and robustness of the network.

Some of the more important parameters in terms of training and network capacity are the number of hidden neurons, the learning rate and the momentum parameter.

These neurons are essentially hidden from view, and their number and organization can typically be treated as a black box to people who are interfacing with the system.

Square root of the sum of squared differences between the network targets and actual outputs divided by number of patterns (only for training by minimum error).

Deep learning

Deep learning (also known as deep structured learning or hierarchical learning) is part of a broader family of machine learning methods based on learning data representations, as opposed to task-specific algorithms.

Deep learning architectures such as deep neural networks, deep belief networks and recurrent neural networks have been applied to fields including computer vision, speech recognition, natural language processing, audio recognition, social network filtering, machine translation, bioinformatics, drug design and board game programs, where they have produced results comparable to and in some cases superior to human experts.&#91;4&#93;&#91;5&#93;&#91;6&#93;

Deep learning models are vaguely inspired by information processing and communication patterns in biological nervous systems yet have various differences from the structural and functional properties of biological brains (especially human brain), which make them incompatible with neuroscience evidences.&#91;7&#93;&#91;8&#93;&#91;9&#93;

Most modern deep learning models are based on an artificial neural network, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in deep belief networks and deep Boltzmann machines.&#91;11&#93;

The universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions.&#91;15&#93;&#91;16&#93;&#91;17&#93;&#91;18&#93;&#91;19&#93;

By 1991 such systems were used for recognizing isolated 2-D hand-written digits, while recognizing 3-D objects was done by matching 2-D images with a handcrafted 3-D object model.

But while Neocognitron required a human programmer to hand-merge features, Cresceptron learned an open number of features in each layer without supervision, where each feature is represented by a convolution kernel.

In 1994, André de Carvalho, together with Mike Fairhurst and David Bisset, published experimental results of a multi-layer boolean neural network, also known as a weightless neural network, composed of a 3-layers self-organising feature extraction neural network module (SOFT) followed by a multi-layer classification neural network module (GSN), which were independently trained.

In 1995, Brendan Frey demonstrated that it was possible to train (over two days) a network containing six fully connected layers and several hundred hidden units using the wake-sleep algorithm, co-developed with Peter Dayan and Hinton.&#91;39&#93;

Simpler models that use task-specific handcrafted features such as Gabor filters and support vector machines (SVMs) were a popular choice in the 1990s and 2000s, because of ANNs' computational cost and a lack of understanding of how the brain wires its biological networks.

The principle of elevating 'raw' features over hand-crafted optimization was first explored successfully in the architecture of deep autoencoder on the 'raw' spectrogram or linear filter-bank features in the late 1990s,&#91;48&#93;

Many aspects of speech recognition were taken over by a deep learning method called long short-term memory (LSTM), a recurrent neural network published by Hochreiter and Schmidhuber in 1997.&#91;50&#93;

showed how a many-layered feedforward neural network could be effectively pre-trained one layer at a time, treating each layer in turn as an unsupervised restricted Boltzmann machine, then fine-tuning it using supervised backpropagation.&#91;58&#93;

The impact of deep learning in industry began in the early 2000s, when CNNs already processed an estimated 10% to 20% of all the checks written in the US, according to Yann LeCun.&#91;67&#93;

was motivated by the limitations of deep generative models of speech, and the possibility that given more capable hardware and large-scale data sets that deep neural nets (DNN) might become practical.

However, it was discovered that replacing pre-training with large amounts of training data for straightforward backpropagation when using DNNs with large, context-dependent output layers produced error rates dramatically lower than then-state-of-the-art Gaussian mixture model (GMM)/Hidden Markov Model (HMM) and also than more-advanced generative model-based systems.&#91;59&#93;&#91;70&#93;

offering technical insights into how to integrate deep learning into the existing highly efficient, run-time speech decoding system deployed by all major speech recognition systems.&#91;10&#93;&#91;72&#93;&#91;73&#93;

In 2010, researchers extended deep learning from TIMIT to large vocabulary speech recognition, by adopting large output layers of the DNN based on context-dependent HMM states constructed by decision trees.&#91;75&#93;&#91;76&#93;&#91;77&#93;&#91;72&#93;

In 2009, Nvidia was involved in what was called the “big bang” of deep learning, “as deep-learning neural networks were trained with Nvidia graphics processing units (GPUs).”&#91;78&#93;

In 2014, Hochreiter's group used deep learning to detect off-target and toxic effects of environmental chemicals in nutrients, household products and drugs and won the 'Tox21 Data Challenge' of NIH, FDA and NCATS.&#91;87&#93;&#91;88&#93;&#91;89&#93;

Although CNNs trained by backpropagation had been around for decades, and GPU implementations of NNs for years, including CNNs, fast implementations of CNNs with max-pooling on GPUs in the style of Ciresan and colleagues were needed to progress on computer vision.&#91;80&#93;&#91;81&#93;&#91;34&#93;&#91;90&#93;&#91;2&#93;

In November 2012, Ciresan et al.'s system also won the ICPR contest on analysis of large medical images for cancer detection, and in the following year also the MICCAI Grand Challenge on the same topic.&#91;92&#93;

In 2013 and 2014, the error rate on the ImageNet task using deep learning was further reduced, following a similar trend in large-scale speech recognition.

For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as 'cat' or 'no cat' and using the analytic results to identify cats in other images.

Over time, attention focused on matching specific mental abilities, leading to deviations from biology such as backpropagation, or passing information in the reverse direction and adjusting the network to reflect that information.

Neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.

Despite this number being several order of magnitude less than the number of neurons on a human brain, these networks can perform many tasks at a level beyond that of humans (e.g., recognizing faces, playing 'Go'&#91;99&#93;

The user can review the results and select which probabilities the network should display (above a certain threshold, etc.) and return the proposed label.

The extra layers enable composition of features from lower layers, potentially modeling complex data with fewer units than a similarly performing shallow network.&#91;11&#93;

The training process can be guaranteed to converge in one step with a new batch of data, and the computational complexity of the training algorithm is linear with respect to the number of neurons involved.&#91;115&#93;&#91;116&#93;

that involve multi-second intervals containing speech events separated by thousands of discrete time steps, where one time step corresponds to about 10 ms.

DNNs have proven themselves capable, for example, of a) identifying the style period of a given painting, b) 'capturing' the style of a given painting and applying it in a visually pleasing manner to an arbitrary photograph, and c) generating striking imagery based on random visual input fields.&#91;128&#93;&#91;129&#93;

Word embedding, such as word2vec, can be thought of as a representational layer in a deep learning architecture that transforms an atomic word into a positional representation of the word relative to other words in the dataset;

Finding the appropriate mobile audience for mobile advertising is always challenging, since many data points must be considered and assimilated before a target segment can be created and used in ad serving by any ad server.&#91;161&#93;&#91;162&#93;

'Deep anti-money laundering detection system can spot and recognize relationships and similarities between data and, further down the road, learn to detect anomalies or classify and predict specific events'.

Deep learning is closely related to a class of theories of brain development (specifically, neocortical development) proposed by cognitive neuroscientists in the early 1990s.&#91;166&#93;&#91;167&#93;&#91;168&#93;&#91;169&#93;

These developmental models share the property that various proposed learning dynamics in the brain (e.g., a wave of nerve growth factor) support the self-organization somewhat analogous to the neural networks utilized in deep learning models.

Like the neocortex, neural networks employ a hierarchy of layered filters in which each layer considers information from a prior layer (or the operating environment), and then passes its output (and possibly the original input), to other layers.

Other researchers have argued that unsupervised forms of deep learning, such as those based on hierarchical generative models and deep belief networks, may be closer to biological reality.&#91;173&#93;&#91;174&#93;

researchers at The University of Texas at Austin (UT) developed a machine learning framework called Training an Agent Manually via Evaluative Reinforcement, or TAMER, which proposed new methods for robots or computer programs to learn how to perform tasks by interacting with a human instructor.&#91;165&#93;

Such techniques lack ways of representing causal relationships (...) have no obvious ways of performing logical inferences, and they are also still a long way from integrating abstract knowledge, such as information about what objects are, what they are for, and how they are typically used.

systems, like Watson (...) use techniques like deep learning as just one element in a very complicated ensemble of techniques, ranging from the statistical technique of Bayesian inference to deductive reasoning.'&#91;190&#93;

As an alternative to this emphasis on the limits of deep learning, one author speculated that it might be possible to train a machine vision stack to perform the sophisticated task of discriminating between 'old master' and amateur figure drawings, and hypothesized that such a sensitivity might represent the rudiments of a non-trivial machine empathy.&#91;191&#93;

In further reference to the idea that artistic sensitivity might inhere within relatively low levels of the cognitive hierarchy, a published series of graphic representations of the internal states of deep (20-30 layers) neural networks attempting to discern within essentially random data the images on which they were trained&#91;193&#93;

Learning a grammar (visual or linguistic) from training data would be equivalent to restricting the system to commonsense reasoning that operates on concepts in terms of grammatical production rules and is a basic goal of both human language acquisition&#91;199&#93;

Such a manipulation is termed an “adversarial attack.” In 2016 researchers used one ANN to doctor images in trial and error fashion, identify another's focal points and thereby generate images that deceived it.

Another group showed that certain psychedelic spectacles could fool a facial recognition system into thinking ordinary people were celebrities, potentially allowing one person to impersonate another.

ANNs can however be further trained to detect attempts at deception, potentially leading attackers and defenders into an arms race similar to the kind that already defines the malware defense industry.

ANNs have been trained to defeat ANN-based anti-malware software by repeatedly attacking a defense with malware that was continually altered by a genetic algorithm until it tricked the anti-malware while retaining its ability to damage the target.&#91;201&#93;

The various types of neural networks are explained and demonstrated, applications of neural networks like ANNs in medicine are described, and a detailed historical background is provided.

It is composed of a large number of highly interconnected processing elements (neurones) working in unison to solve specific problems.

Minsky and Papert, published a book (in 1969) in which they summed up a general feeling of frustration (against neural networks) among researchers, and was thus accepted by most without further analysis.

For a more detailed description of the history click here The first artificial neuron was produced in 1943 by the neurophysiologist Warren McCulloch and the logician Walter Pits.

Neural networks, with their remarkable ability to derive meaning from complicated or imprecise data, can be used to extract patterns and detect trends that are too complex to be noticed by either humans or other computer techniques.

The network is composed of a large number of highly interconnected processing elements(neurones) working in parallel to solve a specific problem.

Even more, a large number of tasks, require systems that use a combination of the two approaches (normally a conventional computer is used to supervise the neural network) in order to perform at maximum efficiency.

In the human brain, a typical neuron collects signals from others through a host of fine structures called dendrites.

The neuron sends out spikes of electrical activity through a long, thin stand known as an axon, which splits into thousands of branches.

At the end of each branch, a structure called a synapse converts the activity from the axon into electrical effects that inhibit or excite activity from the axon into electrical effects that inhibit or excite activity in the connected neurones.

When a neuron receives excitatory input that is sufficiently large compared with its inhibitory input, it sends a spike of electrical activity down its axon.

However because our knowledge of neurones is incomplete and our computing power is limited, our models are necessarily gross idealisations of real networks of neurones.

In the using mode, when a taught input pattern is detected at the input, its associated output becomes the current output.

If the input pattern does not belong in the taught list of input patterns, the firing rule is used to determine whether to fire or not.

The rule goes as follows: Take a collection of training patterns for a node, some of which cause it to fire (the 1-taught set of patterns) and others which prevent it from doing so (the 0-taught set).

Then the patterns not in the collection cause the node to fire if, on comparison , they have more input elements in common with the 'nearest' pattern in the 1-taught set than with the 'nearest' pattern in the 0-taught set.

For example, a 3-input neuron is taught to output 1 when the input (X1,X2 and X3) is 111 or 101 and to output 0 when the input is 000 or 001.

It differs from 000 in 1 element, from 001 in 2 elements, from 101 in 3 elements and from 111 in 2 elements.

Therefore the firing rule gives the neuron a sense of similarity and enables it to respond 'sensibly' to patterns not seen during training.

If we represent black squares with 0 and white squares with 1 then the truth tables for the 3 neurones after generalisation are;

Top neuron Middle neuron Bottom neuron &#160;From the tables it can be seen the following associasions can be extracted:

Feedback architectures are also referred to as interactive or recurrent, although the latter term is often used to denote feedback connections in single-layer organisations.

The commonest type of artificial neural network consists of three groups, or layers, of units: a layer of &quot;input&quot;

The activity of each hidden unit is determined by the activities of the input units and the weights on the connections between the input and the hidden units.

The weights between the input and hidden units determine when each hidden unit is active, and so by modifying these weights, a hidden unit can choose what it represents.

The single-layer organisation, in which all units are connected to one another, constitutes the most general case and is of more potential computational power than hierarchically structured multi-layer organisations.

The perceptron (figure 4.4) turns out to be an MCP model ( neuron with weighted inputs ) with some additional, fixed, pre--processing.

Units labelled A1, A2, Aj , Ap are called association units and their task is to extract specific, localised featured from the input images.

The book was very well written and showed mathematically that single layer perceptrons could not do some basic pattern recognition operations like determining the parity of a shape or determining whether a shape is connected or not.

associative mapping in which the network learns to produce a particular pattern on the set of input units whenever another particular pattern is applied on the set of input units.

This is used to provide pattern completition, ie to produce a pattern whenever a portion of it or a distorted pattern is presented.

nearest-neighbour recall, where the output pattern produced corresponds to the input pattern stored, which is closest to the pattern presented, and interpolative recall, where the output pattern is a similarity dependent interpolation of the patterns stored corresponding to the pattern presented.

Yet another paradigm, which is a variant associative mapping is classification, ie when there is a fixed set of categories into which the input patterns are to be classified.

Whereas in asssociative mapping the network stores the relationships among patterns, in regularity detection the response of each unit has a particular 'meaning'.

Supervised learning which incorporates an external teacher, so that each output unit is told what its desired response to input signals ought to be.

important issue conserning supervised learning is the problem of error convergence, ie the minimisation of error between the desired and computed unit values.

For threshold units, the output is set at one of two levels, depending on whether the total input is greater than or less than some threshold value.

Sigmoid units bear a greater resemblance to real neurones than do linear or threshold units, but all three must be considered rough approximations.

To make a neural network that performs some specific task, we must choose how the units are connected to one another (see figure 4.1), and we must set the weights on the connections appropriately.

We can teach a three-layer network to perform a particular task by using the following procedure: Assume that we want a network to recognise hand-written digits.

The network would therefore need 256 input units (one for each sensor), 10 output units (one for each kind of digit) and a number of hidden units.

For each kind of digit recorded by the sensors, the network should produce high activity in the appropriate output unit and low activity in the other output units.

To train the network, we present an image of a digit and compare the actual activity of the 10 output units with the desired activity.

Next we change the weight of each connection so as to reduce the error.We repeat this training process for many different images of each different images of each kind of digit until the network classifies every image correctly.

To implement this procedure we need to calculate the error derivative for the weight (EW) in order to change the weight by an amount that is proportional to the rate at which the error changes as the weight is changed.

It was developed independently by two teams, one (Fogelman-Soulie, Gallinari and Le Cun) in France, the other (Rumelhart, Hinton and Williams) in U.S. In order to train a neural network to perform some task, we must adjust the weights of each unit in such a way that the error between the desired output and the actual output is reduced.

To compute the EA for a hidden unit in the layer just before the output layer, we first identify all the weights between that hidden unit and the output units to which it is connected.

After calculating all the EAs in the hidden layer just before the output layer, we can compute in like fashion the EAs for other layers, moving from layer to layer in a direction opposite to the way activities propagate through the network.

Since neural networks are best at identifying patterns or trends in data, they are well suited for prediction or forecasting needs including:

Neural networks are ideal in recognising diseases using scans since there is no need to provide a specific algorithm on how to identify the disease.

Diagnosis can be achieved by building a model of the cardiovascular system of an individual and comparing it with the real time physiological measurements taken from the patient.

If this routine is carried out regularly, potential harmful medical conditions can be detected at an early stage and thus make the process of combating the disease much easier.

model of an individual's cardiovascular system must mimic the relationship among physiological variables (i.e., heart rate, systolic and diastolic blood pressures, and breathing rate) at different physical activity levels.

Sensor fusion enables the ANNs to learn complex relationships among the individual sensor values, which would otherwise be lost if the values were individually analysed.

In medical modelling and diagnosis, this implies that even though each sensor in a set may be sensitive only to a specific physiological variable, ANNs are capable of detecting complex medical conditions by fusing the data from the individual biomedical sensors.

trained an autoassociative memory neural network to store a large number of medical records, each of which includes information on symptoms, diagnosis, and treatment for a particular case.

There is also a strong potential for using neural networks for database mining, that is, searching for patterns implicit within the explicitly stored information in databases.

A feedforward neural network is integrated with the AMT and was trained using back-propagation to assist the marketing control of airline seat allocations.

Stephens, 1987] While it is significant that neural networks have been applied to this problem, it is also important to see that this intelligent technology can be integrated with expert systems and other approaches to make a functional system.

Finally, I would like to state that even though neural networks have a huge potential we will only get the best of them when they are intergrated with computing, AI, fuzzy logic and related subjects.

Artificial neural network

The neural network itself isn't an algorithm, but rather a framework for many different machine learning algorithms to work together and process complex data inputs.&#91;2&#93;

For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as 'cat' or 'no cat' and using the results to identify cats in other images.

An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain.

In common ANN implementations, the signal at a connection between artificial neurons is a real number, and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs.

Signals travel from the first layer (the input layer), to the last layer (the output layer), possibly after traversing the layers multiple times.

Artificial neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.

(1943) created a computational model for neural networks based on mathematics and algorithms called threshold logic.

With mathematical notation, Rosenblatt described circuitry not in the basic perceptron, such as the exclusive-or circuit that could not be processed by neural networks at the time.&#91;9&#93;

In 1959, a biological model proposed by Nobel laureates Hubel and Wiesel was based on their discovery of two types of cells in the primary visual cortex: simple cells and complex cells.&#91;10&#93;

Much of artificial intelligence had focused on high-level (symbolic) models that are processed by using algorithms, characterized for example by expert systems with knowledge embodied in if-then rules, until in the late 1980s research expanded to low-level (sub-symbolic) machine learning, characterized by knowledge embodied in the parameters of a cognitive model.&#91;citation needed&#93;

key trigger for renewed interest in neural networks and learning was Werbos's (1975) backpropagation algorithm that effectively solved the exclusive-or problem by making the training of multi-layer networks feasible and efficient.

Support vector machines and other, much simpler methods such as linear classifiers gradually overtook neural networks in machine learning popularity.

As errors propagate from layer to layer, they shrink exponentially with the number of layers, impeding the tuning of neuron weights that is based on those errors, particularly affecting deep networks.

To overcome this problem, Schmidhuber adopted a multi-level hierarchy of networks (1992) pre-trained one level at a time by unsupervised learning and fine-tuned by backpropagation.&#91;24&#93;

(2006) proposed learning a high-level representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine&#91;26&#93;

Once sufficiently many layers have been learned, the deep architecture may be used as a generative model by reproducing the data when sampling down the model (an 'ancestral pass') from the top level feature activations.&#91;27&#93;&#91;28&#93;

In 2012, Ng and Dean created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from YouTube videos.&#91;29&#93;

Earlier challenges in training deep neural networks were successfully addressed with methods such as unsupervised pre-training, while available computing power increased through the use of GPUs and distributed computing.

for very large scale principal components analyses and convolution may create a new class of neural computing because they are fundamentally analog rather than digital (even though the first implementations may use digital devices).&#91;31&#93;

Between 2009 and 2012, recurrent neural networks and deep feedforward neural networks developed in Schmidhuber's research group won eight international competitions in pattern recognition and machine learning.&#91;33&#93;&#91;34&#93;

Researchers demonstrated (2010) that deep neural networks interfaced to a hidden Markov model with context-dependent states that define the neural network output layer can drastically reduce errors in large-vocabulary speech recognition tasks such as voice search.

A team from his lab won a 2012 contest sponsored by Merck to design software to help find molecules that might identify new drugs.&#91;47&#93;

As of 2011&#91;update&#93;, the state of the art in deep learning feedforward networks alternated between convolutional layers and max-pooling layers,&#91;42&#93;&#91;48&#93;

Artificial neural networks were able to guarantee shift invariance to deal with small and large natural objects in large cluttered scenes, only when invariance extended beyond shift, to all ANN-learned concepts, such as location, type (object class label), scale, lighting and others.

An artificial neural network is a network of simple elements called artificial neurons, which receive input, change their internal state (activation) according to that input, and produce output depending on the input and activation.

An artificial neuron mimics the working of a biophysical neuron with inputs and outputs, but is not a biological neuron model.

The network forms by connecting the output of certain neurons to the input of other neurons forming a directed, weighted graph.

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Sometimes a bias term added to total weighted sum of inputs to serve as threshold to shift the activation function.&#91;53&#93;

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The learning rule is a rule or an algorithm which modifies the parameters of the neural network, in order for a given input to the network to produce a favored output.

A common use of the phrase 'ANN model' is really the definition of a class of such functions (where members of the class are obtained by varying parameters, connection weights, or specifics of the architecture such as the number of neurons or their connectivity).

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(commonly referred to as the activation function&#91;55&#93;) is some predefined function, such as the hyperbolic tangent or sigmoid function or softmax function or rectifier function.

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is an important concept in learning, as it is a measure of how far away a particular solution is from an optimal solution to the problem to be solved.

For applications where the solution is data dependent, the cost must necessarily be a function of the observations, otherwise the model would not relate to the data.

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While it is possible to define an ad hoc cost function, frequently a particular cost (function) is used, either because it has desirable properties (such as convexity) or because it arises naturally from a particular formulation of the problem (e.g., in a probabilistic formulation the posterior probability of the model can be used as an inverse cost).

In 1970, Linnainmaa finally published the general method for automatic differentiation (AD) of discrete connected networks of nested differentiable functions.&#91;64&#93;&#91;65&#93;

In 1986, Rumelhart, Hinton and Williams noted that this method can generate useful internal representations of incoming data in hidden layers of neural networks.&#91;71&#93;

The choice of the cost function depends on factors such as the learning type (supervised, unsupervised, reinforcement, etc.) and the activation function.

For example, when performing supervised learning on a multiclass classification problem, common choices for the activation function and cost function are the softmax function and cross entropy function, respectively.

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The network is trained to minimize L2 error for predicting the mask ranging over the entire training set containing bounding boxes represented as masks.

the cost function is related to the mismatch between our mapping and the data and it implicitly contains prior knowledge about the problem domain.&#91;79&#93;

commonly used cost is the mean-squared error, which tries to minimize the average squared error between the network's output,

Minimizing this cost using gradient descent for the class of neural networks called multilayer perceptrons (MLP), produces the backpropagation algorithm for training neural networks.

Tasks that fall within the paradigm of supervised learning are pattern recognition (also known as classification) and regression (also known as function approximation).

The supervised learning paradigm is also applicable to sequential data (e.g., for hand writing, speech and gesture recognition).

This can be thought of as learning with a 'teacher', in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.

The cost function is dependent on the task (the model domain) and any a priori assumptions (the implicit properties of the model, its parameters and the observed variables).

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whereas in statistical modeling, it could be related to the posterior probability of the model given the data (note that in both of those examples those quantities would be maximized rather than minimized).

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The aim is to discover a policy for selecting actions that minimizes some measure of a long-term cost, e.g., the expected cumulative cost.

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because of the ability of Artificial neural networks to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of the original control problems.

Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.

Training a neural network model essentially means selecting one model from the set of allowed models (or, in a Bayesian framework, determining a distribution over the set of allowed models) that minimizes the cost.

This is done by simply taking the derivative of the cost function with respect to the network parameters and then changing those parameters in a gradient-related direction.

convolutional neural network (CNN) is a class of deep, feed-forward networks, composed of one or more convolutional layers with fully connected layers (matching those in typical Artificial neural networks) on top.

recent development has been that of Capsule Neural Network (CapsNet), the idea behind which is to add structures called capsules to a CNN and to reuse output from several of those capsules to form more stable (with respect to various perturbations) representations for higher order capsules.&#91;103&#93;

can find an RNN weight matrix that maximizes the probability of the label sequences in a training set, given the corresponding input sequences.

provide a framework for efficiently trained models&#160;for hierarchical processing of temporal data, while enabling the investigation of the inherent role of RNN layered composition.&#91;clarification needed&#93;

This is particularly helpful when training data are limited, because poorly initialized weights can significantly hinder model performance.

that integrate the various and usually different filters (preprocessing functions) into its many layers and to dynamically rank the significance of the various layers and functions relative to a given learning task.

This grossly imitates biological learning which integrates various preprocessors (cochlea, retina, etc.) and cortexes (auditory, visual, etc.) and their various regions.

Its deep learning capability is further enhanced by using inhibition, correlation and its ability to cope with incomplete data, or 'lost' neurons or layers even amidst a task.

The link-weights allow dynamic determination of innovation and redundancy, and facilitate the ranking of layers, of filters or of individual neurons relative to a task.

LAMSTAR had a much faster learning speed and somewhat lower error rate than a CNN based on ReLU-function filters and max pooling, in 20 comparative studies.&#91;140&#93;

These applications demonstrate delving into aspects of the data that are hidden from shallow learning networks and the human senses, such as in the cases of predicting onset of sleep apnea events,&#91;132&#93;

The whole process of auto encoding is to compare this reconstructed input to the original and try to minimize the error to make the reconstructed value as close as possible to the original.

with a specific approach to good representation, a good representation is one that can be obtained robustly from a corrupted input and that will be useful for recovering the corresponding clean input.

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of the first denoising auto encoder is learned and used to uncorrupt the input (corrupted input), the second level can be trained.&#91;146&#93;

Once the stacked auto encoder is trained, its output can be used as the input to a supervised learning algorithm such as support vector machine classifier or a multi-class logistic regression.&#91;146&#93;

It formulates the learning as a convex optimization problem with a closed-form solution, emphasizing the mechanism's similarity to stacked generalization.&#91;150&#93;

Each block estimates the same final label class y, and its estimate is concatenated with original input X to form the expanded input for the next block.

Thus, the input to the first block contains the original data only, while downstream blocks' input adds the output of preceding blocks.

It offers two important improvements: it uses higher-order information from covariance statistics, and it transforms the non-convex problem of a lower-layer to a convex sub-problem of an upper-layer.&#91;152&#93;

TDSNs use covariance statistics in a bilinear mapping from each of two distinct sets of hidden units in the same layer to predictions, via a third-order tensor.

The need for deep learning with real-valued inputs, as in Gaussian restricted Boltzmann machines, led to the spike-and-slab RBM (ssRBM), which models continuous-valued inputs with strictly binary latent variables.&#91;156&#93;

One of these terms enables the model to form a conditional distribution of the spike variables by marginalizing out the slab variables given an observation.

However, these architectures are poor at learning novel classes with few examples, because all network units are involved in representing the input (a distributed representation) and must be adjusted together (high degree of freedom).

It is a full generative model, generalized from abstract concepts flowing through the layers of the model, which is able to synthesize new examples in novel classes that look 'reasonably' natural.

DPCNs predict the representation of the layer, by using a top-down approach using the information in upper layer and temporal dependencies from previous states.&#91;174&#93;

For example, in sparse distributed memory or hierarchical temporal memory, the patterns encoded by neural networks are used as addresses for content-addressable memory, with 'neurons' essentially serving as address encoders and decoders.

Preliminary results demonstrate that neural Turing machines can infer simple algorithms such as copying, sorting and associative recall from input and output examples.

Approaches that represent previous experiences directly and use a similar experience to form a local model are often called nearest neighbour or k-nearest neighbors methods.&#91;189&#93;

Unlike sparse distributed memory that operates on 1000-bit addresses, semantic hashing works on 32 or 64-bit addresses found in a conventional computer architecture.

These models have been applied in the context of question answering (QA) where the long-term memory effectively acts as a (dynamic) knowledge base and the output is a textual response.&#91;194&#93;

While training extremely deep (e.g., 1 million layers) neural networks might not be practical, CPU-like architectures such as pointer networks&#91;196&#93;

overcome this limitation by using external random-access memory and other components that typically belong to a computer architecture such as registers, ALU and pointers.

The key characteristic of these models is that their depth, the size of their short-term memory, and the number of parameters can be altered independently – unlike models like LSTM, whose number of parameters grows quadratically with memory size.

In that work, an LSTM RNN or CNN was used as an encoder to summarize a source sentence, and the summary was decoded using a conditional RNN language model to produce the translation.&#91;201&#93;

For the sake of dimensionality reduction of the updated representation in each layer, a supervised strategy selects the best informative features among features extracted by KPCA.

The main idea is to use a kernel machine to approximate a shallow neural net with an infinite number of hidden units, then use stacking to splice the output of the kernel machine and the raw input in building the next, higher level of the kernel machine.

The basic search algorithm is to propose a candidate model, evaluate it against a dataset and use the results as feedback to teach the NAS network.&#91;205&#93;

models of how the dynamics of neural circuitry arise from interactions between individual neurons and finally to models of how behavior can arise from abstract neural modules that represent complete subsystems.

These include models of the long-term, and short-term plasticity, of neural systems and their relations to learning and memory from the individual neuron to the system level.

specific recurrent architecture with rational valued weights (as opposed to full precision real number-valued weights) has the full power of a universal Turing machine,&#91;223&#93;

but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.

Supervised neural networks that use a mean squared error (MSE) cost function can use formal statistical methods to determine the confidence of the trained model.

A confidence analysis made this way is statistically valid as long as the output probability distribution stays the same and the network is not modified.

By assigning a softmax activation function, a generalization of the logistic function, on the output layer of the neural network (or a softmax component in a component-based neural network) for categorical target variables, the outputs can be interpreted as posterior probabilities.

Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example and by grouping examples in so-called mini-batches.

No neural network has solved computationally difficult problems such as the n-Queens problem, the travelling salesman problem, or the problem of factoring large integers.

Other than the case of relaying information from a sensor neuron to a motor neuron, almost nothing of the principles of how information is handled by biological neural networks is known.

The motivation behind Artificial neural networks is not necessarily to strictly replicate neural function, but to use biological neural networks as an inspiration.

Alexander Dewdney commented that, as a result, artificial neural networks have a 'something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are.

argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies.

While the brain has hardware tailored to the task of processing signals through a graph of neurons, simulating even a simplified neuron on von Neumann architecture may compel a neural network designer to fill many millions of database rows for its connections&#160;&#8211;&#32;

Schmidhuber notes that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by GPGPUs (on GPUs), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before.&#91;231&#93;

Arguments against Dewdney's position are that neural networks have been successfully used to solve many complex and diverse tasks, ranging from autonomously flying aircraft&#91;233&#93;

Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be 'an opaque, unreadable table...valueless as a scientific resource'.

In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers.

Although it is true that analyzing what has been learned by an artificial neural network is difficult, it is much easier to do so than to analyze what has been learned by a biological neural network.

Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful.

Advocates of hybrid models (combining neural networks and symbolic approaches), claim that such a mixture can better capture the mechanisms of the human mind.&#91;236&#93;&#91;237&#93;

The simplest, static types have one or more static components, including number of units, number of layers, unit weights and topology.

On Monday, January 21, 2019

Lecture 6 | Training Neural Networks I

In Lecture 6 we discuss many practical issues for training modern neural networks. We discuss different activation functions, the importance of data ...